In past and present times, there is a complete consensus among all Muslim jurists and scholars that women are not allowed to lead the Friday Prayer nor can they deliver the Friday khutbah. The logical as well as Shari`ah-based conclusion in this regard is that only men are allowed to perform such a function. The proponents of the weird view referred to in the question depend on evidence from the Sunnah that refers to very specific circumstances where a woman can lead the Prayer inside her home, and has no relation to Friday Prayer and general congregations.
The Assembly of Muslim Jurists in America in this regard has stated that: The Assembly of Muslim Jurists in America (AMJA) totally denounces such an action, which is a complete heresy, and affirms the following facts:
The ultimate reference and the supreme source of legislation of Islam is the Book of Allah, and the purified Sunnah of the Prophet (peace and blessings be upon him). The Prophet (peace and blessings be upon him) is reported to have said, “I left among you that which if you hold on to it you will never go astray after me: the Book of Allah, and my Sunnah.”
Consensus and unanimity on the interpretation of a certain text in these two sources (the Qur’an and the Sunnah) is an irrefutable proof for its meaning and a clear sign and evidence that any other later interpretation is nullified, void, and rejected. Allah Almighty says, (And whoso opposeth the Messenger after the guidance (of Allah) hath been manifested unto him, and followeth other than the believer’s way, We appoint for him that unto which he himself hath turned, and expose him unto hell a hapless journey’s end) (An-Nisaa’ 4:115).
The Prophet (peace and blessings be upon him) described the successful group among the ones that went astray as being those “who follow and behave (after) what I and my Companions follow and behave (after).”
Second, there is unanimous consensus for the entire Ummah, in the east and west, that women cannot lead the Friday Prayer nor can they deliver the sermon. Whoever takes part in such a Prayer, then his Prayer is nullified. It is never found in any jurisprudential text of Hanafis, Malikis, Shafi`is or Hanbalis, nor even from Shiite scholars, that a woman can lead the Friday Prayer or deliver the sermon. This opinion [that a woman can lead the Friday Prayer] is an innovation and a heresy on any account, nullified by all scholars.
Some of the evidences that led to the above-mentioned consensus is what came in the purified Sunnah that the rows of the women should be behind the rows of the men in the Prayer. In the hadith narrated by Anas (may Allah be pleased with him) we learn that the Prophet (peace and blessings be upon him) prayed as imam for Anas, his mother and his aunt, he made Anas stand on his right side and Anas’s mother and his aunt behind them.
The same arrangement was followed in the masjid of the Prophet (peace and blessings be upon him) and across the entire Ummah for centuries. Imam Muslim narrated that the Prophet (peace and blessings be upon him) said that, “The best rows for the men are the front ones and the least good are the ones towards the back; and the best rows for the women are the ones towards the back and the least good are the ones towards the front.” This was for no other reason but to protect them from any embarrassment and to close the door before any evil thoughts or temptations that might come into the hearts of whoever might be looking at them otherwise. How could it be possible then that a woman can be in front of all rows leading the Friday Prayer?
Other evidence is that it is well established in Islamic jurisprudence that Allah has not made Prayer in congregation mandatory for women, neither is it obligatory that women pray Friday Prayers. The Prophet (peace and blessings be upon him) mentioned in the authentic narration through Abu Dawud: “Friday Prayer is mandatory upon each Muslim (to be performed) in a congregation; the only types of people who are exempted are a slave, a woman, a young boy or a sick person.”
In addition, the Prophet (peace and blessings be upon him) informed Muslim women that their Prayer at home is better for them than attending the congregation, out of mercy upon them that they face the hassles of going out and to shield them from temptations. The Prophet (peace and blessings be upon him) said, “Do not prevent the women from going to the masjid; however, it is better for them to pray at home” (Ahmad and Abu Dawud). How could it be possible then that it is not mandatory for a woman to pray in the masjid, to achieve the intent of the Legislator (Allah) of making it easy upon women by praying at home, while shielding them from temptations, then a woman goes up on the pulpit to deliver the sermon, and stands in front of the rows as imam!
It was never recorded that a single woman, across Islamic history, has performed such an action, nor even demanded to do it; not in the time of the Prophet (peace and blessings be upon him), nor in the time of the Companions, or their followers, not even in later generations and centuries. This by itself constitutes a clear proof of the invalidity of this opinion, and anyone who calls for it or helps to implement it is a heretic.
If any of this has legitimacy, the most qualified women to actually do it were the Mothers of the Believers; most of them were knowledgeable brilliant scholars. It is enough to talk about the eloquent, articulate, bright, and knowledgeable of `A’ishah, daughter of Abu Bakr, wife of the Prophet, Mother of the Believers. If there was any shred of evidence that this action is good and permissible, these shining examples among Muslim women would have taken the lead to it. There were numerous women scholars across Islamic history, jurisprudential references and narration experts; they were honest, trustworthy, and experts in what they accomplished. Imam Az-zahabi said, “It was never recorded that a woman propagated false hadith attributed to the Prophet (peace and blessings be upon him).” He also mentioned that “I am not aware of any woman that were accused of propagating falsehoods or ones whose narrations were disregarded.” Among the teachers of Imam Ibn `Asaker were 80 women. The same is for Imam Abu Muslim Al-Farahidi, who reported the narration of 70 women. Imam Shafi`i, Al-Bukhari, Ibn Khalkan, and Ibn Hayyan all had women among their teachers. None of these noble women scholars ever attempted to lead the Friday Prayer nor deliver the sermon, even though they were superior in knowledge over many of their contemporary men in jurisprudence, religious knowledge, and narrations from the Prophet (peace and blessings be upon him).
Muslim women participated in all aspects of Islamic work throughout Islamic history: as scholars and jurisprudential references, as participating in all kinds of worship, as workers in the field of relief and emergency aid, and in the enjoining of good and forbidding of evil. But never were they imams for Friday Prayers or have ever delivered Friday sermons.
It is a logical and Shari`ah-based conclusion that only men are allowed to perform such a function as leading the Friday Prayer and delivering the sermon. Whoever disputes this fact can take as much time as he wants to dig out one single example form the volumes of Islamic jurisprudence across the centuries, and he will miserably fail.
Lastly, those who are calling for such acts are taking as an excuse a narration that Umm Waraqah was given the permission by the Prophet (peace and blessings be upon him) to lead her household members in the Prayer. This narration, even assuming that it is authentic, has nothing to do whatsoever with the Friday Prayer. It is talking about some very specific circumstances where a woman can lead the Prayer inside her home, and has no relation to Friday Prayer and general congregations.
AMJA is delivering this somber warning message to the entire Ummah, not to give any credit to such false initiatives that contradict the basics and fundamentals of the religion, and are totally heretical innovations. AMAJ reminds Muslims that we are to follow only the Book of Allah and the purified Sunnah of the Prophet (peace and blessings be upon him). Muslims should pay careful attention to whom they are seeking the guidance from; indeed, he who strives to cling to his religion nowadays is suffering as much as a person who is trying to keep a tight fist on a piece of flaming charcoal in the palm of his hand. AMAJ is extending a sincere supplication to none but Allah to save us from all trials and tribulations, and to guide us all to that which is closest to the mercy and pleasure of Allah, as He is the only One capable of that. It is Allah alone that we seek in all of our actions, and it is He alone Who can guide to the straight path.